An Algebraic Obstruction to Isomorphism of Markov Shifts with Group Alphabets

Ward, T. B. (1993) An Algebraic Obstruction to Isomorphism of Markov Shifts with Group Alphabets. Bulletin of the London Mathematical Society, 25 (3). pp. 240-246. ISSN 0024-6093

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Abstract

Given a compact group G, a standard construction of a Z2 Markov shift SG with alphabet G is described. The cardinality of G (if G is finite) or the topological dimension of G (if G is a torus) is shown to be an invariant of measurable isomorphism for SG. We show that if G is sufficiently non-abelian (for instance A5, PSL2(F7), or a Suzuki simple group) and H is any abelian group with |H| = |G|, then SG and SH are not isomorphic. Thus the cardinality of G is seen to be necessary but not sufficient to determine the measurable structure of SG.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 14:48
Last Modified:	29 Jun 2025 00:15
URI:	https://ueaeprints.uea.ac.uk/id/eprint/18596
DOI:	10.1112/blms/25.3.240

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